On the Mathematics of Income Inequality: Splitting the Gini Index in Two

Summary: (Adapted from the MathFest 2013 Prizes and Awards Booklet) This article starts with the fact that a certain hedge fund manager earned more in 2010 than 50,000 math professors combined. There follows a graph showing the percent of annual national income received by the top 1% of wage earners since 1913. The authors explore various measurements and characteristics of income inequality.

Robert T. Jantzen is professor of mathematics at Villanova University, straddling the fence between physics and mathematics while working in the field of classical general relativity. Having slipped from mathematics into physics as an undergraduate at Princeton during the golden age of general relativity in the 1970's, his graduate work in physics at UC Berkeley was supervised by Abraham Taub in the mathematics department. He has employed the tools of differential geometry and Lie group theory, first to elucidate properties of spatially homogeneous cosmological models, and later of stationary axisymmetric spacetimes like black holes. A backdrop to this career has been the inspiration of a lifetime of academic commuting to the land of Italian geometers like Luigi Bianchi and Tullio Levi-Civita, now joined by one of their contemporaries, Corrado Gini.

Klaus Volpert is an associate professor at Villanova University. He enjoys teaching pure mathematics for its elegance and beauty, and applied mathematics for its power and urgency, and he is most happy when the two come together. He received the university's Lindback Award for Distinguished Teaching in 2009. His research interests have morphed over time from acoustics (during his high school days in Lindau, Germany) to spectral sequences (in his graduate work with Richard Koch at the University of Oregon) to problems at the intersection of mathematics with economics and finance. Outside of academia his greatest joy is making music with his family, Heewon, Hannah and Peter.